let Omega be non empty set ; :: thesis: for F being SigmaField of Omega holds chi (Omega,Omega) is_random_variable_on F, Borel_Sets
let F be SigmaField of Omega; :: thesis: chi (Omega,Omega) is_random_variable_on F, Borel_Sets
set g2 = chi (Omega,Omega);
reconsider O = Omega as Element of F by PROB_1:5;
chi (O,Omega) is random_variable of F, Borel_Sets by ZZZ;
hence chi (Omega,Omega) is_random_variable_on F, Borel_Sets by RANDOM_3:def 1; :: thesis: verum